Tsinghua University – University of Amsterdam Joint Research Centre for Logic

Invited Talk

  • Title: Learning What Others Know
  • Abstract: I will present recent joint work with A. Baltag in [1] on modelling scenarios in which agents communicate ‘all they know’ (by e.g. giving access to one’s information database to all or some of the other agents), as well as more complex informational events, such as hacking. In these cases we assume that some agent(s) instantly ‘read’ all the information stored at a specific source. Modelling such scenarios requires us to extend the framework of epistemic logics to one in which we abstract away from the specific announcement and formalize directly the action of sharing ‘all you know’ (with some or all of the other agents). In order to do this, I will introduce these sharing ‘all you know’-actions and formalize their effect, i.e. the state of affairs in which one agent (or group of agents) has ‘epistemic superiority’ over another agent (or group). Concrete I capture the epistemic superiority of agents by enriching the language with comparative epistemic assertions for individual and groups of agents (as such extending the comparison-types considered in [5]).Another ingredient that I add to our logical system, is a new modal operator for ‘common distributed knowledge’, used to model situations in which we achieve common knowledge in a larger group of agents by information-sharing only within each of the subgroups. This new concept of ‘common distributed knowledge’ combines features of both common knowledge and distributed knowledge. We position this work in the context of other known work such as: the problem of converting distributed knowledge into common knowledge via acts of sharing [4]; the more semantic approach in [2] on communication protocols requiring agents to ‘tell everybody all they know’; the work on public sharing events with a version of common distributed knowledge in [3]; and the work on resolution actions in [6]. 

[1] A. Baltag and S. Smets, Learning what others know, in L. Kovacs and E. Albert (eds.), LPAR23 proceedings of the International Conference on Logic for Programming, AI and Reasoning, EPiC Series in Computing, 73:90-110, 2020. 

[2] A. Baltag and S. Smets, Protocols for Belief Merge: Reaching Agreement via Communication, Logic Journal of the IGPL, 21(3):468-487, 2013.

[3] A. Baltag, What is DEL good for? Lecture at the ESSLLI2010-Workshop on Logic, Rationality and Intelligent Interaction, 16 August 2010. 

[4] J. van Benthem, One is a lonely number. In P. Koepke Z. Chatzidakis and W. Pohlers, (eds.) Logic Colloquium 2002, 96-129, ASL and A.K. Peters, Wellesley MA, 2002. 

[5] H. van Ditmarsch, W. van der Hoek & B. Kooi,  Knowing More – from Global to Local Correspondence,   Proc. of IJCAI-09, 955–960, 2009. 

[6] T. Agotnes & Y.N. Wang, Resolving Distributed Knowledge, Artificial Intelligence, 252: 1–21, 2017.